JERUSALEM (Reuters) - Former Israeli President Shimon Peres remains in a critical condition 24 hours after suffering a massive stroke, but is showing signs of improvement, his doctors said on Wednesday.

Peres, 93, is still sedated and on a respirator, said Yitshak Kreiss, director of the Sheba Medical Center near Tel Aviv. But he is "a bit more aware" and "we can see some improvement", Kreiss told reporters.

"We are trying to reduce some of the sedation in order to evaluate him, and that's a good sign," he said.

Peres' son-in-law and personal physician Rafi Valdan said earlier in the day it was too soon to tell whether there was lasting neurological damage from the stroke that afflicted the right side of Peres' brain, but the broader health indicators were good.

Peres, former president and prime minister, won the Nobel Peace Prize in 1994. He has had minor health problems over the past year while maintaining a busy public schedule.

He held regular meetings on Tuesday and appeared in "perfect condition", Valdan said, before suffering headaches. He was taken to hospital for an examination and then suffered what Valdan described as a "massive stroke".

INDUCED COMA

When doctors briefly revived him from a medically induced coma, Valdan said, Peres was responsive, squeezing his hand and speaking a few words.

Peres has been a part of almost every major development in Israel since the country's founding in 1948. In a career spanning nearly 70 years, he has served in a dozen cabinets and was twice a Labour prime minister.

He ran for office five times between 1977 and 1996, but never won a national election outright.

He shared the Nobel Peace Prize with Israel's former Prime Minister Yitzhak Rabin and late Palestinian leader Yasser Arafat for reaching, in 1993, an interim peace deal which never hardened into a lasting treaty.

Rabin was assassinated in 1995 by a far-right Israeli who opposed the peace deal, and it was Peres who took over as prime minister after Rabin's death.

At the next election, despite polls showing him far ahead, Peres lost to rightist Likud leader Benjamin Netanyahu by fewer than 30,000 votes.

Valdan said he did not believe there was an imminent threat to Peres' life, but called it a difficult time for the family.

"We are very close to him," he said. "We are very moved and touched by his condition, but also very moved by the reaction of the Israeli public."